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The National Collegiate Athletic Association — or to most of us, the NCAA — recently came down hard on Division III athletic powerhouse (snicker) California Institute of Technology for using “ineligible” players. Sanctions were meted out, and all is just.

Except, it isn’t really. It turns out that at Caltech, one of the most prestigious schools in the U.S., students are allowed to essentially try out a class, or “shop” it, for the first three weeks of the semester prior to formally enrolling (or dropping) said class. And unfortunately for Caltech, that meant the students were “technically” ineligible — but not actually sitting around playing video games in the dorms.

I won’t take pot-shots at the anachronistic NCAA — The New York Times’ Joe Nocera already is doing a great job on that score. But the situation does have me wondering: Wouldn’t it be nice if newly named CEOs had the same trial option before enrolling or dropping that Caltech students enjoy?

Imagine getting three weeks to settle into the big chair, take a look around, listen in at the water cooler, talk to some customers, then decide how to proceed. I suspect some recent CEO hires might have some second thoughts as they approached the three-week deadline:

Ron Johnson, J.C. Penney

J.C. Penney (NYSE:JCP) CEO Ron Johnson came from perhaps the best retailer of the millennium, Apple (NASDAQ:AAPL), where he and the company were wildly successful.

Sometime within the first three weeks of his move to Dallas, he must’ve learned that JCP customers were just as loyal as those at Apple — just for a different reason: bargain prices vs. cutting-edge products. J.C. Penney’s shoppers go there for the discounts available on specific days, and the even deeper bargains available on whatever day suits the store managers. They don’t want “brands,” they don’t want in-store stores, they want deals — basically the antithesis of Apple store customers.

Despite a huge payday, Johnson would’ve been forgiven for realizing he might not be a perfect fit, and bolting.

Scott Thompson, Yahoo

The CEO chair at Yahoo! (NASDAQ:YHOO) still was warm four months after Carol Bartz was let go when Scott Thompson, president of eBay‘s (NASDAQ:EBAY) PayPal unit, was tapped for the role.

PayPal and its parent eBay were (and are) stable and growing. Yahoo! — well before the Bartz experiment — was unstable and not growing.

Thompson stepped into a maelstrom of “What to do?” suggestions, which one would’ve expected given the junker he took over.

The problem was, most of the questions were about attrition. Sell the company even though they’d already rebuffed an offer from Microsoft (NASDAQ:MSFT), sell part of it to private investors, or sell off assets like their stake in Alibaba (consider that done). Meanwhile, nobody asked Thompson — who was chief technology officer at PayPal with no real online ad-revenue generation experience — how he would grow, or salvage, a flagging business model.

Thompson might have considered taking a hike considering that deep-seated negativity. Of course, he didn’t have to wait long to leave, anyway — Yahoo! dropped Thompson after just a few months. Now, Yahoo is Marissa Mayers’ problem.

James Hughes, First Solar

In May, James Hughes went from chief commercial officer at First Solar (NASDAQ:FSLR) to CEO. That’s quite a bump in pay and prestige, although perhaps the job description suggests he should’ve had a better feel for the company pulse.

However, Hughes previously was the CEO at Advance Energy (NASDAQ:AEI), a power plants and natural gas player. Those are solid and sound assets, and a stable source of income. Solar is totally next-generation technology that currently relies heavily on subsidies to keep the lights on.

On the same day he was named CEO, May 3, the company put a positive spin on future earnings … while at the same time announcing quarterly losses and layoffs — usually never a cause for celebration.

And if Hughes hadn’t noticed the crummy worldwide market for solar panels during his time as CCO, surely he’d have gotten an idea how tough the solar market was by the three-week mark — FSLR shares shed more than 20% in less than a month, and some analysts were predicting single-digit prices by year’s end.

Honorable Mention

OK, you get a bonus pick — one other CEO who took the reins this year might have thought twice early on.

Petrobras‘ (NYSE:PBR) Maria das Graças Foster started in February 2012 on the heels of miserable earnings. Then the company suffered an oil spill — its third in three months — the day she took over. And while it would’ve been too late, watching the YPF disaster unfold in nearby Argentina would’ve given the willies to anyone doing business where governmental interference is a real possibility.

Marc Bastow is an Assistant Editor at InvestorPlace.com. As of this writing, he was long MSFT and AAPL.